Maximum Score Path in Grid

You are given an n x m grid of integers. Your task is to find the maximum score obtainable by moving from the top-left cell to the bottom-right cell. At each step, you are allowed to move only to the right or downward.

The score of a path is defined as the sum of the values of the cells visited. The recurrence relation for the dynamic programming solution is given by:

[ \text{dp}[i,j] = \max(\text{dp}[i-1,j],, \text{dp}[i,j-1]) + A[i,j] ]

where A[i,j] denotes the value in the cell at the i-th row and j-th column (using 0-indexing). It is guaranteed that n and m are positive integers, and the grid may contain negative values.

inputFormat

The first line contains two integers n and m, representing the number of rows and columns of the grid respectively. This is followed by n lines, each containing m space-separated integers representing the grid's values.

outputFormat

Output a single integer which is the maximum score achievable from the top-left corner to the bottom-right corner.

3 3
5 3 2
1 2 1
1 1 5

16